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111.
We test the efficiency of three minimization algorithms as applied to models of peptides and proteins. These include: the limited memory quasi-Newton (L-BFGS) of Liu and Nocedal; the truncated Newton (TN) with automatic preconditioner of Nash; and the nonlinear conjugate gradients (CG) of Shanno and Phua. The molecules are modeled by two energy functions, one is the Gromos 87 united atoms force field (defining the energy EGRO), which takes into account the intramolecular interactions only; the second is defined by the energy Etot=EGRO+Esolv, where Esolv is an implicit solvation free every term based on the solvent-accessible surface area of the atoms. The molecules studied are cyclo-(d -Pro1–Ala2–Ala3–Ala4–Ala5) (31 atoms), axinastatin 2 [cyclo-(Asn1–Pro2–Phe3–Val4–Leu5–Pro6–Val7), 62 atoms], and the protein bovine pancreatic trypsin inhibitor (58 residues, 568 atoms). With EGRO, the performance of TN with respect to the CPU time is found to be ∼1.2 to 2 times better than that of both L-BFGS and CG, whereas, with Etot, L-BFGS outperforms TN by a factor of 1.5 to 2.5, and CG by a larger factor. Still, the quality of the solution in terms of the value of the minimized energy and the gradient norm, obtained with TN, is always equivalent to, or better than, those obtained with L-BFGS and CG. The performance is analyzed in terms of criteria outlined by Nash and Nocedal. We find the distribution of the Hessian eigenvalues to be a reliable predictor of efficiency. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 354–364, 1999 相似文献
112.
电力系统中地网腐蚀诊断的一种新的数学模型及其仿真计算 总被引:1,自引:0,他引:1
对电力系统中具有重大应用价值的地网腐蚀诊断问题抽象出仿真求解的一种新的数学模型:即求解带约束的非线性隐式方程组模型.但由于问题本身的物理特性决定了所建立的数学模型具有以下特点:一是非线性方程组为欠定方程组,而且非线性程度非常高;二是方程组的所有函数均为隐函数;三是方程组附加若干箱约束条件.这种特性给模型分析与算法设计带来巨大困难.对于欠定方程组的求解,文中根据工程实际背景,尽可能地扩充方程的个数,使之成为超定方程组,然后对欠定方程组和超定方程组分别求解并进行比较.将带约束的非线性隐函数方程组求解问题,转化为无约束非线性最小二乘问题,并采用矩阵求导等技术和各种算法设计技巧克服隐函数的计算困难,最后使用拟牛顿信赖域方法进行计算.大量的计算实例表明,文中所提出的数学模型及求解方法是可行的.与目前广泛采用的工程简化模型相比较,在模型和算法上具有很大优势. 相似文献
113.
基于修正拟牛顿方程,利用Goldstein-Levitin-Polyak(GLP)投影技术,建立了求解带凸集约束的优化问题的两阶段步长非单调变尺度梯度投影算法,证明了算法的全局收敛性和一定条件下的Q超线性收敛速率.数值结果表明新算法是有效的,适合求解大规模问题. 相似文献
114.
Metric-based SR1 updates which are stabilized by a variationalrelaxation of the quasi-Newton relation are examined. Thisinvestigation reveals an interesting and surprising connection to theorigin of quasi-Newton methods as first formulated by Davidon [1]. Anextended version of Davidon's original direct prediction SR1 updateis shown to be self-complementary and to possess a finite terminationproperty on quadratics, and limited-memory versions of the update areshown to be globally convergent. Variants of this update are testednumerically and compared to several other metric-based SR1 variantsand the BFGS update. Finally, metric-based stabilizations of the SR1update are critiqued in general, and a promising new model-basedstrategy recently developed is briefly described. 相似文献
115.
Issam A. R. Moghrabi 《Journal of Mathematical Modelling and Algorithms》2007,6(2):231-238
The authors have derived what they termed quasi-Newton multi step methods in [2]. These methods have demonstrated substantial numerical improvements over the standard single step Secant-based BFGS. Such
methods use a variant of the Secant equation that the updated Hessian (or its inverse) satisfies at each iteration. In this
paper, new methods will be explored for which the updated Hessians satisfy multiple relations of the Secant-type. A rational
model is employed in developing the new methods. The model hosts a free parameter which is exploited in enforcing symmetry
on the updated Hessian approximation matrix thus obtained. The numerical performance of such techniques is then investigated
and compared to other methods. Our results are encouraging and the improvements incurred supercede those obtained from other
existing methods at minimal extra storage and computational overhead. 相似文献
116.
Ramos A.M. Glowinski R. Periaux J. 《Journal of Optimization Theory and Applications》2002,112(3):499-516
This article is concerned with the numerical solution of multiobjective control problems associated with nonlinear partial differential equations and more precisely the Burgers equation. For this kind of problems, we look for the Nash equilibrium, which is the solution to a noncooperative game. To compute the solution of the problem, we use a combination of finite-difference methods for the time discretization, finite-element methods for the space discretization, and a quasi-Newton BFGS algorithm for the iterative solution of the discrete control problem. Finally, we apply the above methodology to the solution of several tests problems. To be able to compare our results with existing results in the literature, we discuss first a single-objective control problem, already investigated by other authors. Finally, we discuss the multiobjective case. 相似文献
117.
本文对于求解非线性方程组 F (x) =0的 Broyden秩 1第二种方法的计算格式进行修正 ,在算法实现过程中使用了δ2 -加速技巧 ,从而大大提高了算法的收敛速度 . 相似文献
118.
119.
Vera L. R. Lopes José Mario Martínez 《Numerical Functional Analysis & Optimization》2013,34(9-10):1193-1209
We develop a theory of quasi-New ton and least-change update methods for solving systems of nonlinear equations F(x) = 0. In this theory, no differentiability conditions are necessary. Instead, we assume that Fcan be approximated, in a weak sense, by an affine function in a neighborhood of a solution. Using this assumption, we prove local and ideal convergence. Our theory can be applied to B-differentiable functions and to partially differentiable functions. 相似文献
120.
通过引入基于最小改变的对角修正策略,结合三阶拟牛顿方程,提出了基于Armijo线搜索的对角三阶拟柯西法.在适当的假设下,算法保证了修正矩阵的非奇异性,并证明了算法的线性收敛性.数值试验表明该算法是有效的. 相似文献